It doesn't matter if the country changes, as long as the capital remains the new countries capital
Rome is certainly a strong candidate -- for all recorded history, excluding very transitory military occupations, it has been capital of its own city state, regional nation among many other Italian nations (early Roman Kingdom, the Papal States), the Roman Empire, and/or a unified Italian nation.
Depens on what terms: A capital of a continious sovereign state Or a capital of multiple states, which possible intervals during which that city wasn't a capital.
Category 1 would be I guess Damascus. Catergory 2 I would nominate either London or Paris, but maybe I'm Eurocentric.
Anyone willing to add are welcome!